乘法的

First, basing on point halving, this thesis proposed a new efficient algorithm of computing kP lQ on an elliptic curve over the finite field with characteristic 2 and analyzed the computational efficiency. When the ratio I/M of inversion to multiplication cost is small, this new algorithm is about 5%～30% faster than the traditional algorithms.

首先，基于半点运算给出一种计算特征为2的有限域上椭圆曲线双标量乘法kP lQ的新算法并分析了效率，当基域上求乘法与求逆的运算时间的比值比较小时，新算法的效率比已有算法提高5％～30％。

The method this paper discussed was based following theoretic analysis: Square and multiplication of large integer are two basic operations in modular exponential m_ary algorithm. The main operations of m_ary algorithm of point multiplication in elliptic curve encryption were doublings and point addition. The steps of m_ary algorithm in point multiplication was similar to modular exponential.

其基于以下理论分析：模幂m_ary算法的基本运算为大数乘法，其中包括大数平方算法和一般大数乘法；椭圆曲线加密算法中点乘的m_ary算法步骤与模幂的m_ary算法相同，后者的基本运算为倍乘和加法。

Experiments on multiplier tree and adder tree expressions exhibit running time reduction of 83% to 99%, and 40% to 80% respectively.4. Arithmetic unit check with half adder graph technique: Binary Moment Diagram technique has been used in multiplier equivalence checking.

比如针对加法和乘法连续运算的表达式，算法从实现电路中提取变量顺序和结合顺序并加以利用，实验表明，在验证乘法连续运算的表达式时减少了83%～99%的时间，加法连续运算表达式的验证时间也可减少40%～89%。4。

Based on the foregoing strategy, we choose Inverse Modified Discrete Cosine Transform and Polyphase Synthesis Filterband of the MP3 decoder by an ASIC implementation. Moreover, to further reduce the hardware cost, we use CORDIC-based calculations and merging some arithmetic operations to replace the original ones of IMDCT and PSF.

基於前述的原则及由运算量的统计分析，我们选定「反转修正式离散余弦转换(Inverse Modified Discrete Cosine Transform， IMDCT)」与「多相位合成滤波频带(Polyphase Synthesis Filterband， PSF)」使用ASIC方式实现，同时为了有效降低这两个模组的硬体成本，我们导入「座标轴旋转数位计算机」及合并运算方式取代原始算术运算，使得新的计算式有效降低原IMDCT约74%之乘法及约49%加法运算，而在多相位合成滤波频带的反离散余弦转换也有降低约33.4%之乘法及约24.6%之加法运算。

The Recursive Least Square based on Lethe gene, Partial Least Square, BP Nerve Network,which are wide applied in process control, are discussed detailedly respectively. The characteristic and their domain applicable fields of each model and their mend models are systematically analysed.

对在过程控制领域广泛应用的渐消记忆递推最小二乘法、偏最小二乘法和BP 神经网络等建模方法进行了详细的讨论，并对每种建模方法及其改进算法的特性、应用范围进行了深入的分析。

Finally, the fact is proved using mathematical induction and the character of stochastic matrix.

首先介绍了防御矩阵的概念、物理意义、重要性质及计算方法，分析了防御矩阵满足乘法交换律的重要意义，最后综合运用数学归纳法和随机矩阵性质证明了防御矩阵满足乘法交换律的事实，此结论无论对于多层防御系统的防御效用值研究连是矩阵理论研究都有一定的指导作用。

We use Hodges-Lehmann statistic to do significance test for those factors. The multiplication model is applied in the quantitative analysis and weighted least squares method is introduced to solve the multiplication model. Although the matrix of coefficients is not of full rank and the solutions of the multiplication model are not unique, we prove that all those solutions are equivalent in some sense.

本文用Hodges-Lehmann统计量对风险因子作显著性检验，将乘法模型用于数据修匀和风险因子的定量分析中，并提出了用加权最小二乘法求解风险因子的风险度量，在系数矩阵不满秩、解不唯一的情况下证明了所有解在某种意义下的等价性。

By replacing pseudo-Mersenne numbers with generalized Mersenne numbers, we propose a new notion-Generalized Optimal Extension Fields, and study the fast arithmetic about multiplication and modular arithmetic in GOEFs.

利用广义Mersenne数代替伪Mersenne数，提出了广义最优扩域的概念，并研究其上的快速乘法运算和取模运算，为乘法运算给出了通用的复杂度公式，为取模运算给出了具体的运算公式，推广了Bailey，Mihailescu和Woodbury等在最优扩域上的相应结果。

On the other hand, the known number in multiplication becomes the unknown number in division.

在乘法中已知的，在除法中变成未知的；在乘法中是未知的，在除法中变成已知的。

Thetic devices that look so real, most people don't notice they're there.2 A painter by training, Barron designs pores, veins a=(100+2)×43 atients. The finding means that Alzheimer's, which affects 4 million Americans and millions more around the world, may be diagn

在此基础上引导学生观察这类题目的特点，以及怎样应用乘法分配律，从而使学生明确：两个数相乘，把其中一个比较接近整十、整百、整千的数改写成一个整十、整百、整千的数与一个数的和，再应用乘法分配律可以使计算简便。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了